NGC 3311 is the central cD galaxy of the Hydra I cluster. We use globular clusters around NGC 3311, combined with kinematical data of the galaxy itself, to investigate the dark matter distribution in the central region of Hydra I. Radial velocities of 118 bright globular clusters, based on VLT/VIMOS mask spectroscopy, are used to calculate velocity dispersions which are well defined out to 100 kpc. NGC 3311 is the most distant galaxy for which this kind of study has been performed. We also determine velocity dispersions of the stellar component from long slit spectroscopy out to 20 kpc. Moreover, we present a new photometric model for NGC 3311 in the V-band. We search for a dark halo which in the context of a spherical Jeans model. We also compare the radial velocity distributions of globular clusters and planetary nebulae. The projected stellar velocity dispersion rises from 185 km/s to 350 km/s at a radius of 20 kpc. The globular cluster dispersion rises as well from 500 km/s at 10 kpc to about 800 km/s at 100 kpc, comparable to the velocity dispersion of the cluster galaxies. A dark matter halo with a core reproduces well the velocity dispersions of stars and globular clusters simultaneously under isotropy. The central stellar velocity dispersions predicted by cosmological NFW halos are less good representations, while the globular clusters allow a wide range of halo parameters. A suspected radial anisotropy of the stellar population aggravates the deviations. However, we find discrepancies with previous kinematical data, which we cannot resolve and may indicate a more complicated velocity pattern. Although one cannot conclusively demonstrate that the dark matter halo of NGC 3311 has a core rather than a cusp, a core seems to be preferred by the present data. A more complete velocity field and an analysis of the anisotropy is required to reach firm conclusions.
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